CN113793369B - Complex free-form surface iterative bidirectional normal projection registration method - Google Patents
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Abstract
The invention belongs to the technical field of complex free surface point cloud data registration, and in the field of three-dimensional high-precision automatic registration, the existing improved algorithm widens the performance of an original ICP algorithm to a certain extent under certain conditions, but the influence of an initial position on algorithm convergence and the search and calculation of a corresponding relation still remain bottleneck problems of the algorithm; the invention provides a complex free-form surface iterative bi-directional normal projection registration method, which provides different coarse registration realization algorithms based on inherent geometric features of data in a coarse registration link. The accurate registration method is established on a classical ICP algorithm frame, and is improved aiming at establishment of a corresponding relation and elimination of pseudo corresponding point pairs.
Description
Technical Field
The invention belongs to the technical field of complex free-form surface point cloud data registration, and particularly relates to a complex free-form surface iterative bi-directional normal projection registration method.
Background
Registration technology has been a research hotspot for many years, and registration is a fundamental and key link in the fields of computer vision, digital image processing, pattern recognition, reverse engineering and the like. In the measurement and detection of a complex curved surface, the measurement difficulty of the complex free curved surface is high, and in the data acquisition process, it is difficult to acquire all required data in the same pose of a measured object by using a sensor. Registration is needed between measurement data under different poses and visual angles, and the data obtained by different sensors also needs to consider the problem of data fusion. The purpose of registration is to achieve unification between the different coordinate systems. In the measurement inspection of complex curved surfaces, unification among measurement coordinate systems and design coordinate systems is a basis and a premise for ensuring the effectiveness of error evaluation. It is a high precision automatic registration problem. Since the ICP algorithm was proposed, it is gradually the most widely applied method in the field of high-precision automatic registration due to its excellent performance. However, in theory, the ICP algorithm converges to a local minimum in the sense of square distance scale, and the algorithm has high requirement on the initial position, and can ensure the convergence direction only by providing an initial value close to a global minimum, so as to obtain a global optimal solution for surface registration. The original ICP algorithm has strong constraint requirements on the inclusion relationship of two sets of point clouds, i.e., the algorithm requires that all or a large proportion of one of the two point clouds be a subset of the other, otherwise the final convergence result will be affected, and even a mismatching occurs. In addition, the ICP algorithm is a computationally intensive method, the computational overhead is considered in practical application, and the objective function of the method is built on the square term of all data point errors, so that the proportion of local errors is amplified in the registration process. The advantages of the ICP algorithm are outstanding, the defects are clear, and the ICP algorithm and a related variant method thereof occupy the mainstream position in the field of three-dimensional high-precision automatic registration at present. However, the existing improved algorithm can broaden the performance of the original ICP algorithm to a certain extent under certain conditions, and the influence of the initial position on the convergence condition of the algorithm and the searching and calculating of the corresponding relation still remain bottleneck problems of the algorithm.
Disclosure of Invention
The invention overcomes the defects existing in the prior art, and solves the technical problems that: the invention provides a complex free-form surface iterative bi-directional normal projection registration method, which aims at establishing a corresponding relation and eliminating pseudo corresponding point pairs to improve an ICP algorithm.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a complex free-form surface iterative bi-directional normal projection registration method comprises the following steps:
step 1: coarse registration of point set P1 and point set P2: calculating curvature information Cur (Q) of each data point in the point set P1 and the point set P2 i ) And normal angle information ang (Q) i ) The method comprises the steps of carrying out a first treatment on the surface of the Generating feature descriptors fea (Q) containing curvature information and normal angle information for each data point in the point sets P1 and P2 i ) The method comprises the steps of carrying out a first treatment on the surface of the According to feature descriptors fea (Q i ) Data points Q 'and M' participating in registration in point set P1 and point set P2 are filtered according to curvature and methodDetermining corresponding point pairs on two planes by the line included angles, and calculating a transformation matrix according to a quaternion method;
step 2: fine registration of point set P1 and point set P2: establishing a preselected corresponding point according to a bidirectional normal vector projection method, wherein the forward projection result is thatThe result of the back projection is +.>For a pair ofPerforming pseudo-correspondence elimination, and retaining forward correspondence satisfying the condition>For a pair ofPerforming false correspondence elimination; if the data are processed in blocks, sequentially carrying out pseudo-correspondence rejection on each block of data; obtaining a corresponding point set Q k And M k The number of the corresponding point pairs is N k The method comprises the steps of carrying out a first treatment on the surface of the Calculating rotation matrix R according to singular value decomposition method k Translation vector t k The method comprises the steps of carrying out a first treatment on the surface of the Performing data transformation: q (Q) k+1 ＝R k Q k +t k The method comprises the steps of carrying out a first treatment on the surface of the Calculating the error amount: />If d k+1 Delta is less than or equal to, and registration is completed; if d k+1 ＞δ，d k -d k+1 Setting up a preselected corresponding point again to calculate if epsilon is greater than or equal to the maximum iteration number kmax, delta is a given threshold value of average error of the corresponding point, epsilon is the change amount of error in two adjacent iterations; otherwise, the iteration is terminated.
Further, in step 1, at any point Q i Internally implicit feature descriptors of (a)Wherein (1)>Is a coefficient corresponding to the curvature; by->Calculate Q i Normal vector included angle with all neighborhood points, where Q j Is Q i Is a neighborhood point of Q j And Q i The normal vector included angle between them is recorded as +.>Q i 、Q j The normal vector at n i 、n j Obtaining Q i Normal angle information->Q j ∈nbhd(Q i )，nbhd(Q i ) Is Q i Is defined, the k adjacent points of (a).
Further, in step 1, for any point Q in the point set P1 i If fea (Q i ) > kappa, then Q i Selecting a data point set M ', kappa in the point set P2 to be used for registration as a set threshold value for one point in a data point set Q' in the point set P1 to be used for registration; if Q' i With M' j Satisfy the following requirementsThen Q' i With M' j Kappa for the corresponding point pair of point set P1 and point set P2 curv For a set curvature threshold, κ ang Is a set normal angle threshold.
Further, in step 2, the method for establishing the pre-selected corresponding point according to the bi-directional normal vector projection method is as follows: fitting NURBS passing through the point set P1 and the point set P2 to form curved surface fragments, and enabling S to be 1 (u，v)、S 2 (u, v) is a group of corresponding NURBS curved surface pieces on two NURBS fitting curved surfaces, and the curved surface pieces of the two point sets are respectively solved in the data points (u i ，v i ) Units atThe normal vector is:S u (u i ，v i ) And S is v (u i ，v i ) Tangent lines of the NURBS curved surface in the u direction and the v direction respectively; calculating a curved surface S 1 (u, v) at data point { Q 1 ，Q 2 ，...，Q h Normal vector n at } A And curved surface S 2 The intersection point B of (u, v), point B being the point A on the curved surface S 2 A preselected corresponding point on (u, v); at S 2 (u, v) selecting points B' from the vicinity of the selected points B at random, and calculating the curved surface S according to the above method 2 (u, v) normal vector at B' and curved surface S 1 Intersection a' of (u, v); finish from point B' to surface S 1 Back-projecting on (u, v), points B ', a' then being a pair of preselected corresponding points determined by back-projecting; for S 1 H points { Q } (u, v) 1 ，Q 2 ，...，Q h Sequentially performing the above-mentioned bidirectional normal projection, wherein the preselected corresponding point pair established by the forward projection is { (Q) i ，M i ) I=1, 2,..h }, the preselected correspondence established by the back projection is { (M }' i ，Q′ i )，i＝1，2，...，h}。
Further, in step 2, the method for deleting the pseudo corresponding point pair is as follows: for any set of bi-directional projection results (Q i ，M i ) And (M' i ，Q′ i ): in the curved surface S 1 (u, v) Point Q i 、Q′ i The distance between them is dist (Q) i -Q′ i ) The method comprises the steps of carrying out a first treatment on the surface of the In the curved surface S 2 (u, v) Point M i 、M′ i The distance between them is dist (M i -M′ i ) If any one set of bi-directional projection results (Q i ，M i ) And (M' i ，Q′ i ) Satisfy constraint |dist (Q) i -Q′ i )-dist(M i -M′ i ) If eta is not more than eta, eta is a set threshold value (Q i ，M i ) And (M' i ，Q′ i ) The feature information contained is similar, contributing the same to subsequent registration, preserving positive correspondence (Q i ，M i ) Subsequent calculation is carried out, and pseudo corresponding point pairs (M 'are removed' i ，Q′ i )。
Compared with the prior art, the invention has the following beneficial effects:
1. the coarse registration method based on the geometric inherent characteristics has no requirement on the initial positions of the two groups of data, is not strict in constraint on overlapping areas, and has good universality. In addition, the initial screening of the descriptors based on the curvature information and the angle information can effectively delete the data, well reserve the points with obvious geometric features, and therefore the calculation amount of the establishment of the corresponding relation is reduced.
2. According to the method, surface fitting is respectively carried out on measured point cloud data and design point cloud data, preselected corresponding point pairs of two curved surfaces are determined by adopting a bidirectional normal projection method, pseudo corresponding relations are eliminated by utilizing curved surface continuity constraint, distance constraint and curvature constraint, and coordinate transformation relations are calculated according to the obtained corresponding point pairs. Compared with the prior registration algorithm, the method has the advantage that accurate automatic registration of the measurement data and the design data can be realized under the condition that the original data does not contain the corresponding relation.
Drawings
Fig. 1 is a main flow of an ICP improvement algorithm based on bi-directional normal projection.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments; all other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the invention discloses a complex free-form surface iterative bi-directional normal projection registration method, which comprises the following steps:
step 1: coarse registration of point set P1 and point set P2: calculating each number in the point set P1 and the point set P2Curvature information Cur (Q) i ) And normal angle information ang (Q) i ) The method comprises the steps of carrying out a first treatment on the surface of the Generating feature descriptors fea (Q) containing curvature information and normal angle information for each data point in the point sets P1 and P2 i ) The method comprises the steps of carrying out a first treatment on the surface of the According to feature descriptors fea (Q i ) Screening data points Q 'and M' which participate in registration in the point set P1 and the point set P2, determining corresponding point pairs on two planes according to curvature and normal included angles, and calculating a transformation matrix according to a quaternion method; any point Q i Internally implicit feature descriptors of (a)Wherein (1)>Is a coefficient corresponding to the curvature; set Q j Is Q i Is marked as +.>Q i 、Q j The normal vector at n i 、n j Then (I)>Calculate Q i Normal vector included angles with all neighborhood points to obtain Q i Normal angle information->Q j ∈nbhd(Q i )，nbhd(Q i ) Is Q i Is defined, the k adjacent points of (a).
For any point Q in the point set P1 i If fea (Q i ) > kappa, then Q i Selecting a data point set M ', kappa in the point set P2 to be used for registration as a set threshold value for one point in a data point set Q' in the point set P1 to be used for registration; if Q' i With M' j Satisfy the following requirementsThen Q' i With M' j Is a point setCorresponding point pair, κ, of P1 and point set P2 curv For a set curvature threshold, κ ang Is a set normal angle threshold.
Step 2: fine registration of point set P1 and point set P2: the method for establishing the preselected corresponding point according to the bi-directional normal vector projection method comprises the following steps: fitting NURBS passing through the point set P1 and the point set P2 to form curved surface fragments, and enabling S to be 1 (u，v)、S 2 (u, v) is a group of corresponding NURBS curved surface pieces on two NURBS fitting curved surfaces, and the curved surface pieces of the two point sets are respectively solved in the data points (u i ，v i ) The unit normal vector at this point is:S u (u i ，v i ) And S is v (u i ，v i ) Tangent lines of the NURBS curved surface in the u direction and the v direction respectively; calculating a curved surface S 1 (u, v) at data point { Q 1 ，Q 2 ，...，Q h Normal vector n at } A And curved surface S 2 The intersection point B of (u, v), point B being the point A on the curved surface S 2 A preselected corresponding point on (u, v); at S 2 (u, v) selecting points B' from the vicinity of the selected points B at random, and calculating the curved surface S according to the above method 2 (u, v) normal vector at B' and curved surface S 1 Intersection a' of (u, v); finish from point B' to surface S 1 Back-projecting on (u, v), points B ', a' then being a pair of preselected corresponding points determined by back-projecting; for S 1 H points { Q } (u, v) 1 ，Q 2 ，...，Q h Sequentially performing the above-mentioned bidirectional normal projection, wherein the preselected corresponding point pair established by the forward projection is { (Q) i ，M i ) I=1, 2,..h }, the preselected correspondence established by the back projection is { (M }' i ，Q′ i ) I=1, 2,..and h }, the result of forward projection is +.>The result of the back projection is +.>For->Performing pseudo-correspondence elimination, and retaining forward correspondence satisfying the condition>For->The method for eliminating the pseudo correspondence and deleting the pseudo correspondence point pairs comprises the following steps: for any set of bi-directional projection results (Q i ，M i ) And (M' i ，Q′ i ): in the curved surface S 1 (u, v) Point Q i 、Q′ i The distance between them is dist (Q) i -Q′ i ) The method comprises the steps of carrying out a first treatment on the surface of the In the curved surface S 2 (u, v) Point M i 、M′ i The distance between them is dist (M i -M′ i ) If any one set of bi-directional projection results (Q i ，M i ) And (M' i ，Q′ i ) Satisfy constraint |dist (Q) i -Q′ i )-dist(M i -M′ i ) If eta is not more than eta, eta is a set threshold value (Q i ，M i ) And (M' i ，Q′ i ) The feature information contained is similar, contributing the same to subsequent registration, preserving positive correspondence (Q i ，M i ) Subsequent calculation is carried out, and pseudo corresponding point pairs (M 'are removed' i ，Q′ i ) The method comprises the steps of carrying out a first treatment on the surface of the If the data are processed in blocks, sequentially carrying out pseudo-correspondence rejection on each block of data; obtaining a corresponding point set Q k And M k The number of the corresponding point pairs is N k The method comprises the steps of carrying out a first treatment on the surface of the Calculating rotation matrix R according to singular value decomposition method k Translation vector t k The method comprises the steps of carrying out a first treatment on the surface of the Performing data transformation: q (Q) k+1 ＝R k Q k +t k The method comprises the steps of carrying out a first treatment on the surface of the Calculating the error amount:if d k+1 Delta is less than or equal to, and registration is completed; if d k+1 Delta, delta is given corresponding point averageThreshold of error, d k -d k+1 Epsilon is the change amount of the error amount in two adjacent iterations, and the maximum iteration number kmax is not reached, and the establishment of a preselected corresponding point is restarted to calculate; otherwise, the iteration is terminated.
In order to ensure the precision, the automation degree and the universality of complex curved surface detection, the invention provides a high-precision automatic registration method. The registration process inherits the classical concept from coarse to fine, and different coarse registration realization algorithms are given out based on the inherent geometric characteristics of the data in the coarse registration link. The accurate registration method is established on the classical ICP algorithm framework, and the ICP algorithm is improved aiming at the establishment of the corresponding relation and the rejection of the pseudo corresponding point pairs. In the registration process, registration between data points is converted into registration between 'fitting patches' by adopting a curved surface fitting technology, hidden characteristic information is utilized to a greater extent, registration accuracy is high, and the provided coarse registration method can meet the requirements of initial values under different conditions.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (3)
1. The complex free-form surface iterative bi-directional normal projection registration method is characterized by comprising the following steps of:
step 1: coarse registration of point set P1 and point set P2: calculating curvature information Cur (Q) of each data point in the point set P1 and the point set P2 i ) And normal angle information ang (Q) i ) The method comprises the steps of carrying out a first treatment on the surface of the Generating an intrinsic feature descriptor fea (Q) containing curvature information and normal angle information for each data point in the point set P1 and the point set P2 i ) The method comprises the steps of carrying out a first treatment on the surface of the According to intra-intrinsic feature descriptor fea (Q i ) Screening data participating in registration in point set P1 and point set P2The point Q 'and the data point M' are used for determining corresponding point pairs on two planes according to curvature and normal included angles, and calculating a transformation matrix according to a quaternion method;
step 2: fine registration of point set P1 and point set P2: establishing a preselected corresponding point according to a bidirectional normal vector projection method, wherein the forward projection result is thatThe result of the back projection is +.>For a pair ofPerforming pseudo-correspondence elimination, and retaining forward correspondence satisfying the condition>If the data are processed in blocks, sequentially carrying out pseudo-correspondence rejection on each block of data; obtaining a corresponding point set Q k And M k The number of the corresponding point pairs is N k The method comprises the steps of carrying out a first treatment on the surface of the Calculating rotation matrix R according to singular value decomposition method k Translation vector t k The method comprises the steps of carrying out a first treatment on the surface of the Performing data transformation: q (Q) k+1 ＝R k Q k +t k The method comprises the steps of carrying out a first treatment on the surface of the Calculating the error amount: />If d k+1 Delta is less than or equal to, and registration is completed; if d k+1 ＞δ，d k -d k+1 Setting up a preselected corresponding point again to calculate if epsilon is greater than or equal to the maximum iteration number kmax, delta is a given threshold value of average error of the corresponding point, epsilon is the change amount of error in two adjacent iterations; otherwise, terminating the iteration; in the step 2, the method for establishing the preselected corresponding point according to the bi-directional normal vector projection method comprises the following steps: fitting NURBS passing through the point set P1 and the point set P2 to form curved surface fragments, and enabling S to be 1 (u,v)、S 2 (u, v) is a group of corresponding NURBS curved surface pieces on two NURBS fitting curved surfaces, respectivelyThe surface patch solving the two point sets is set at data point (u i ,v i ) The unit normal vector at this point is: />S u (u i ,v i ) And S is v (u i ,v i ) Tangent lines of the NURBS curved surface in the u direction and the v direction respectively; calculating a curved surface S 1 (u, v) at data point { Q 1 ,Q 2 ,...,Q h Normal vector n at } A And curved surface S 2 The intersection point B of (u, v), point B being the point A on the curved surface S 2 A preselected corresponding point on (u, v); at S 2 (u, v) selecting points B' from the vicinity of the selected points B at random, and calculating the curved surface S according to the above method 2 (u, v) normal vector at B' and curved surface S 1 Intersection a' of (u, v); finish from point B' to surface S 1 Back-projecting on (u, v), points B ', a' then being a pair of preselected corresponding points determined by back-projecting;
for S 1 H points { Q } (u, v) 1 ,Q 2 ,...,Q h Sequentially performing the above-mentioned bidirectional normal projection, wherein the preselected corresponding point pair established by the forward projection is { (Q) i ,M i ) I=1, 2,..h }, the preselected correspondence established by the back projection is { (M }' i ,Q′ i ),i＝1,2,...,h}；
In the step 2, the method for deleting the pseudo corresponding point pair is as follows: for any set of bi-directional projection results (Q i ,M i ) And (M' i ,Q′ i ): in the curved surface S 1 (u, v) Point Q i 、Q′ i The distance between them is dist (Q) i -Q′ i ) The method comprises the steps of carrying out a first treatment on the surface of the In the curved surface S 2 (u, v) Point M i 、M′ i The distance between them is dist (M i -M′ i ) If any one set of bi-directional projection results (Q i ,M i ) And (M' i ,Q′ i ) Satisfy constraint dist (Q i -Q′ i )-dist(M i -M′ i ) If eta is not more than eta, eta is a set threshold value (Q i ,M i ) And (M' i ,Q′ i ) The characteristic information contained is similarContribute equally to subsequent registration, preserving positive correspondence (Q i ,M i ) Subsequent calculation is carried out, and pseudo corresponding point pairs (M 'are removed' i ,Q′ i )。
2. The complex freeform surface iterative bi-directional normal projection registration method according to claim 1, wherein in step 1, any point Q i Intra-intrinsic feature descriptor fea (Q) i )＝ang(Q i )+θ cur Cur(Q i ) Wherein θ cur Is a coefficient corresponding to the curvature; by passing throughCalculate Q i Normal vector included angle with all neighborhood points, where Q j Is Q i Is a neighborhood point of Q j And Q i The normal vector included angle between them is recorded as +.> Q i 、Q j The normal vector at n i 、n j Obtaining Q i Normal angle information->Q j ∈nbhd(Q i )，nbhd(Q i ) Is Q i Is defined, the k adjacent points of (a).
3. The method according to claim 1, wherein in the step 1, for any point Q in the point set P1 i If fea (Q i ) > kappa, then Q i Selecting a data point set M ', kappa in the point set P2 to be used for registration as a set threshold value for one point in a data point set Q' in the point set P1 to be used for registration; if Q' i With M' j Satisfy the following requirementsThen Q' i With M' j Kappa for the corresponding point pair of point set P1 and point set P2 curv For a set curvature threshold, κ ang Is a set normal angle threshold.
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